Converting strain maps into elasticity maps for materials with small contrast

Abstract eng:
This study focuses on the quantitative reconstruction of heterogeneous distributions of isotropic elastic moduli from full strain field data. A local reconstruction procedure is developed here for materials with small contrast. Within the framework of the integral formulation of the linear elasticity problem, first-order asymptotics are investigated. Properties of the featured infinite-body Green’s operator are studied to characterize its local and non-local contributions to the volume integral equations considered. On this basis, the combination of multiple strain field solutions corresponding to well-chosen applied macroscopic strains yields a set of local and uncoupled equations relating, respectively, bulk and shear moduli to the spherical and deviatoric components of the strain fields. Valid for any material configuration at first-order in the small contrast limit, such relations permit pointwise conversions of strain maps into elasticity maps. A set of examples illustrates the use of these local equations for parameters identification from full-field data.

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